What is the solution for y^{''}+25y=30sin(5t) ?

The solution for y^{''}+25y=30sin(5t) is y=c_{1}cos(5t)+c_{2}sin(5t)-3tcos(5t)

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y^{''}+25y=30sin(5t)

y^{^{''}} + 25 y = 30 sin (5 t)

y = c_{1} cos (5 t) + c_{2} sin (5 t) - 3 t cos (5 t)

Solution steps

y^{''} (t) + 25 y = 30 sin (5 t)

Solve linear ODE:

y = c_{1} cos (5 t) + c_{2} sin (5 t) - 3 t cos (5 t)

y = c_{1} cos (5 t) + c_{2} sin (5 t) - 3 t cos (5 t)

\frac{d}{d x} (ln (x + x^{2} - 12))

(x^{4} + 2 x^{3} y^{2}) d x + x^{4} y d y = 0

\frac{d y}{d t} - 2 y = 3 e^{- 2 t}, y (0) = 10

\frac{\partial}{\partial x} (x^{3} + 2 x^{2} y + x + 2 y)

\int \frac{1}{X ^{2}} D X d X

What is the solution for y^{''}+25y=30sin(5t) ?
The solution for y^{''}+25y=30sin(5t) is y=c_{1}cos(5t)+c_{2}sin(5t)-3tcos(5t)